They Both Test The Tower

"I suppose so... Are you sure that you want me here while you test it? I don't exactly have the best luck as Link can attest."

"C'mon, it'd be fine! Plus, this is a historic moment! Think of how a teleporter would change the world! Your the Princess! You need to be part of such a historic moment! Plus, I seem to recall you always going out on adventures before Ganon showed up. Your really going to get rid of that adventurous side of yours now that he's gone?"

"Hmm... Alright, you convinced me. Lets do it!" There was a chance that things could go wrong, but she trusted Purah and Purah did mention that she tested the teleporter on a chicken first to make sure it was safe. Part of her did want to put a stop to the experiment though. Not because she was afraid, but because she wanted to learn everything about how she got the Sheikah tower to teleport them anywhere and not just another tower.

Those questions could wait for after they got back. For now, she let Purah set things up.

Purah already had their destination in mind. A stable a few miles away from the Tower near the castle. If things went well, they'd be able to teleport to the stable, rent a horse, and ride all the way back before the day ended.

She took a photo of herself and Zelda and zoomed in to take a photo of the stable. The photos were important to let the tower know who to send and where. And, Purah accidentally forgot to click send on the photo of the stable. The tower only had the photos of her and Zelda and knew who to send, but didn't have a photo for where.

So, when the tower was activated, the two of them was launched to a completely random location, completely naked. Their clothes left behind as a completely separate glitch.